Using 2D Finite Element Analysis to create a sub-surface plane/curve in Xdisp

1. Introduction

Carrying out a two dimensional (2D) finite element (FE) analysis specific for the proposed

installation of a retaining wall and subsequent retained cut excavation is one method to enable

the user to create sub-surface ground movement plane in Xdisp.

A 2D analysis would typically calculate ground movements considering either a plane strain

or axi-symmetric assumption.

One of the main advantages of importing sub-surface planes of displacement from FE

analysis is that the ground movement results can be combined with movements from other

excavations such as those from tunnels calculated by Xdisp. The combined effect can then be

appraised and impacts on 3rd

party assets such as buildings, utilities or tunnels appraised.

Other uses could be to generate an estimate of three dimensional displacements around a deep

basement excavation from a two dimensional analysis based upon an empirical methodology

that has been programmed into Xdisp.

The term ‘ground movement plane’ in this section of text is used to describe a vertical plane

or grid of settlement or horizontal ground movement results. These can be tabulated in terms

of the x and y co-ordinate of the displacement calculation point and magnitude of

displacement.

2D FE analyses generally model a number of construction stages and any of these could be

input into Xdisp dependent upon the desired ground movement results required. Sub-surface

planes of displacement from different stages can be imported into Xdisp, for instance to

reflect the effect of installing piles or completion of the excavation.

Care should be taken if using results from two or more stages from the FE analysis that the

cumulated displacements proposed for use in Xdisp are appropriate. For instance, unless

displacements are zeroed at a given stage of a FE analysis, displacements are carried through

from previous stages.

Consideration should also be given to the use of appropriate soil models in the FE analysis

that has been calibrated to the ground conditions and enable appropriate calculation of ground

movements.

Several common applications are anticipated for importing sub-surface planes of

displacement from a 2D finite element analyses. These include:

• Modelling installation of an embedded retaining wall. Often a stage is included in a

finite element analysis prior to installing the retaining wall for relaxation of the

ground as a consequence of wall installation. The user of Xdisp could then apply the

calculated plane to the length of wall specified in Xdisp

• Modelling excavation induced displacements from an axi-symmetric shaft analysis.

The user of Xdisp could then apply the calculated planes of displacement around the

defined shaft position in Xdisp.

• Modelling excavation induced displacements from a basement or embedded retaining

wall analysis. Where a plane strain 2D analysis has been carried out and the corners

of an excavation are considered to have a stiffening effect, the empirical method

proposed by Fuentes & Devriendt (2010) has been programmed into Xdisp to allow

an estimate of three dimensional displacements to be calculated around the proposed

excavation.

Procedures are provided below for the import of displacements from a 2D FE analysis for

import of pile installation and excavation induced embedded retaining wall analysis.

These would be used to create the sub surface curves as detailed below.

2. Procedure for generating a ‘Sub surface plane’ for the installation of the wall 1. Progress to the construction sequence showing the installation of the wall

2. Query the x and y displacements at a grid of points behind and below the retaining

wall

3. Create an Excel file with the following columns:

• Point number

• x co-ordinate

• y co-ordinate

• vertical displacement

• horizontal displacement

4. Calculate the distance from wall and depth of the points using the co-ordinates

5. For the vertical sub-surface curve, calculate:

a. Distance from wall/wall depth

b. Depth/wall depth

c. Vertical displacement/wall depth

6. For the horizontal sub-surface curve, calculate:

a. Distance from wall/wall depth

b. Depth/wall depth

c. Horizontal displacement/wall depth

The values required for one point are shown graphically in Figure 1.

The values from 5. and 6. would be pasted into the ‘Ground Movement Curves’ tab in

gateway to create the ground movement plane (Figure 2).

This uses the ratios created in the sub-surface plane and applies them to walls of any depth, as

per the base level specified in the ‘Polygonial Excavations’ tab. To model the installation, the

base level specified in Xdisp would be the toe of the installed wall..

Excavation D

epth

Wall

Depth

Depth

Distance from Wall

An appropriate order of x and y polynomial should be selected to obtain an appropriate fit to

the imported data. A check should be carried out to confirm the polynomials proposed in

Xdisp adequately replicate the input data.

Figure 2 – Xdisp input for sub-surface curve

3. Sub surface curve for the excavation 1. Progress to the construction sequence showing the excavation

2. Query the x and y displacements at a grid of points behind and below the retaining

wall

3. Create an Excel file with the following columns:

• point number

• x co-ordinate

• y co-ordinate

• vertical displacement

• horizontal displacement

4. Calculate the distance from wall and depth of the points using the co-ordinates

5. For the vertical sub-surface curve, calculate:

a. Distance from wall/excavation depth

b. Depth/excavation depth

c. Vertical displacement/excavation depth

6. For the horizontal sub-surface curve, calculate:

a. Distance from wall/excavation depth

b. Depth/excavation depth

c. Horizontal displacement/excavation depth

The values required for one point are shown graphically in Figure 1.

The values from 5. and 6. would be pasted into the sub-surface curve tab in gateway to create

the curve (Figure 2).

To model the excavation, the base level specified in Xdisp would be the base of the

excavation (not the installed wall).

An appropriate order of x and y polynomial should be selected to obtain an appropriate fit to

the imported data. A check should be carried out to confirm the polynomials proposed in

Xdisp adequately replicate the input data.